Uniform Materials and the Multiplicative Decomposition of the Deformation Gradient in Finite Elasto-Plasticity

Abstract

In this work we analyze the relation between the multiplicative decomposition F = F^eF^p of the deformation gradient as a product of the elastic and plastic factors and the theory of uniform materials. We prove that postulating such a decomposition is equivalent to having a uniform material model with two configurations – total φ and the inelastic φ₁.

We introduce strain tensors characterizing different types of evolutions of the material and discuss the form of the internal energy and that of the dissipative potential. The evolution equations are obtained for the configurations (φ, φ₁) and the material metric g.

Finally, the dissipative inequality for the materials of this type is presented. It is shown that the conditions of positivity of the internal dissipation terms related to the processes of plastic and metric evolution provide the anisotropic yield criteria.